Inhalt

•  
   Abstract
•  
   Contents
•  
   Introduction
•  
  Exclusive Non-leptonic B Decays
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   QCD Factorization
•  
   Factorization Formula for Two-body Decays
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   BD in QCDF
•  
   QCDF for Three-body Decays
•  
   Alternative Approaches
•  
   Effective Hamiltonian for Weak Decays
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   NNLO corrections to the decay BD
•  
  Soft Collinear Effective Theory and Matching
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   Introduction to SCET
•  
   Scaling of the Fields
•  
   Leading Power SCET Lagrangian
•  
   BD in SCET
•  
  Derivation of the Master Formula
•  
   Matching
•  
   Perturbative Contributions
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   Tree-level and One-loop
•  
   Two-loop
•  
  Simplification of the Two-loop Amplitudes
•  
   Passarino-Veltman Decomposition
•  
   Scalar Integrals
•  
   Integration by Part Identities and Laporta Algorithm
•  
   Reduction of Dirac Matrices to Operators
•  
  Evaluation of the Master Integrals
•  
   The Master Integrals
•  
   Feynman Parameters and Hypergeometric Functions
•  
   Mellin-Barnes Representation
•  
   Numerical Evaluation with MB.m
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   Automated Derivation of MB Representations with AMBRE.m
•  
  Differential Equations
•  
   Harmonic Polylogarithms and HPL.m
•  
   Evaluation of the Integrals
•  
   Differential Equations and Canonical Basis
•  
   Goncharov Polylogarithms
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   Canonical Basis
•  
   Solving Differential Equations
•  
   Checks
•  
  Results and Phenomenological Applications
•  
  Hard Scattering Kernels
•  
   Renormalization Factors and Matching Coefficients
•  
   Discussion of the Results for the Hard Kernels
•  
  Perturbative Amplitude a1
•  
   Hadronic Matrix Elements and Definition of a1
•  
   Results and Dependence on Input Parameters
•  
   Branching Ratios
•  
  Factorization Tests
•  
   Ratios of Non-leptonic Decay Rates
•  
   Ratios of Non-leptonic and Semi-leptonic Decay Rates
•  
   Summary and Discussion
•  
   B in QCD factorization
•  
  Three-body Decays from QCD
•  
   Identifying Regions in the Dalitz Plot
•  
   Factorization Formula
•  
  Generalized Form Factors and Distribution Amplitudes
•  
   Two-pion Distribution Amplitude
•  
   Generalized Form Factor
•  
   The Central Region of the Dalitz Plot
•  
   Leading Order Feynman Diagrams
•  
   Differential Decay Rate
•  
   The Collinear Regions of the Dalitz Plot
•  
   Reconstructing the Dalitz Plot
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   Conclusion and Outlook
•  
   Appendix
•  
   Laporta Reduction of a Sample Feynman Diagram
•  
  Reduction of the bold0mu mumu dest-matrix Algebra to Operators
•  
   Part I: Simplification by a Mathematica Routine
•  
   Part II: Reduction to Known Operators
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   Examples for the Reduction
•  
   Results for the Master Integrals
•  
  Examples of Evaluating Master Integrals
•  
   Hypergeometric Functions: M15
•  
  MB Representations: M23 and M18
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   "Manual" Evaluation of M23
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   Evaluation of M18 by Using AMBRE.m
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   Differential Equations: M4 and M5
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   Canonical Basis: M6 and M7
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  Useful Identities and Definitions for Evaluating Integrals
•  
   Identities for Calculating Feynman Diagrams
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   Cauchy's Residue Theorem and Barnes Lemmas
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   Results for the Feynman Diagrams in the Central Region of the Dalitz Plot
•  
   Bibliography
•  
   Publications and Proceedings
•  
   Acknowledgements